Heisenberg spin chains with additional isotropic three-site exchange interactions

• Published in: arXiv.org 2021-01
• Main Author: Ivanov, N B
• Format: Article
• Language: English
• Subjects: Chains; Couplings; Dimerization; Dimers; Exchanging; Integers; Phases
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2101.05164

The \(J_1-J_3\) Heisenberg spin models with nearest-neighbor (\(J_1\)) and additional isotropic three-site (\(J_3\)) spin interactions remain relatively less explored, although such types of competing exchange terms can naturally emerge from different sources, including the strong-coupling expansion of the multiorbital Hubbard model. Below we present a short survey of the recently published research in this field, the emphasis being on the characteristics of the variety of quantum phases supported by a few generic uniform- and alternating-spin \(J_1-J_3\) Heisenberg chains. For the reason that the positive (\(J_3>0\)) three-site couplings tend towards the formation of local quantum dimers, the \(J_1-J_3\) spin models typically experience some spontaneous dimerization upon increasing \(J_3\). Actually, it occurred that the established dimer phases in spin-\(S\) \(J_1-J_3\) Heisenberg chains (\(S>{1}/{2}\)) serve as complete analogues of the famous gapped Majumdar-Ghosh dimer phase in the spin-\({1}/{2}\) Heisenberg chain with next-nearest-neighbor couplings. The same dimerizations have been observed in the alternating-spin (\(S,\sigma\)) \(J_1-J_3\) chains (\(S>\sigma\)), provided that the cell spin \(S+\sigma=\rm{integer}\), whereas for half-integer cell spin, the local dimer formation produces gapless spin-liquid ground states. The alternating-spin \(J_1-J_3\) chains also provide some typical examples of spin models supporting the so-called non-Lieb-Mattis magnetic phases.